In the present work, the exergy analysis and economic study of 3 different samples of threecomponent mixtures have been investigated (ESI>1, ESI≈1, and ESI<1). The feed mixture has been tested under three different compositions (low, equal, and high contents of the intermediate component). A quantitative comparison between simple and complex configurations, considering thermally coupled, thermodynamically equivalent, and divided-wall column (DWC) has been carried out. The results present that the best sequence could be found by TAC or exergy loss rate analysis. Complex sequences have greater exergy losses in comparison to simple sequences. Despite expectations, the Petlyuk sequence only performs well in a few cases and poorly on others. According to the results, as the amount of intermediate component in the feed increases, both TAC and exergy losses of each sequence increase. The results also demonstrated that the occurrence frequency as the best sequence for DWC, thermodynamically equivalent, thermally coupled, and basic sequences are 36%, 28%, 25%, and 11% respectively. According to authors’ best knowledge, a quantitative exergy and cost comparison (based on rigorous simulation and optimization) between these configurations have never been carried out all together before.

AbstractIn the present work, the exergy analysis and economic study of 3 different samples of threecomponentmixtures have been investigated (ESI>1, ESI≈1, and ESI<1). The feed mixture has beentested under three different compositions (low, equal, and high contents of the intermediatecomponent). A quantitative comparison between simple and complex configurations, consideringthermally coupled, thermodynamically equivalent, and divided-wall column (DWC) has been carriedout. The results present that the best sequence could be found by TAC or exergy loss rate analysis.Complex sequences have greater exergy losses in comparison to simple sequences. Despiteexpectations, the Petlyuk sequence only performs well in a few cases and poorly on others. Accordingto the results, as the amount of intermediate component in the feed increases, both TAC and exergylosses of each sequence increase. The results also demonstrated that the occurrence frequency as thebest sequence for DWC, thermodynamically equivalent, thermally coupled, and basic sequences are36%, 28%, 25%, and 11% respectively. According to authors’ best knowledge, a quantitative exergyand cost comparison (based on rigorous simulation and optimization) between these configurationshave never been carried out all together before.Keywords: Distillation Sequence, Exergy Analysis, Divided-wall Column, Separation Matrix1. IntroductionDistillation process is still the most promising separation technique used in oil, gas, chemical, andpetrochemical industries. But this process in most cases consumes a lot of energy, which is thegreatest part of operating costs in these industries. Thus improving the energy consumption ofdistillation processes is still an interesting field of study.Industrial mixtures commonly contain more than two components and these separation tasks could notbe implemented efficiently in a single column. Hence it is required to employ a number of columnsfor the separation of multicomponent mixtures to the number of desired products. This leads to manypossible configurations (sequences) for separating a multicomponent mixture into relatively pureproducts (sharp split) or several multicomponent product streams (non-sharp or sloppy split). On theother hand, the distillation sequences for separating an n-component feed could be classified inaccordance with the number of distillation columns: having less than n-1 columns (intensified or* Corresponding Author:Email: capepub@cape.iust.ac.irA. H. Khalili-Garakani et al./ Three-component Distillation Columns Sequencing … 67reduced), exactly n-1 columns (basic), or more than n-1 columns (Gridhar et al., 2010). The basicsequences are divided into two categories: simple basic sequences, in which columns have one feedand two products from condenser on top and reboiler at the bottom (direct, indirect); and basiccomplex sequences, in which at least one column has more than one feed or has side products (prefractionator).There are more categories which could be generated from basic configurations: thermally coupled(TC), thermodynamically equivalent (TE), and divided-wall columns (DWC). Figure 1 presents thedifferent categories of three-component distillation sequences. A thermal coupling configurationcould be generated by the substitution of a condenser and/or a reboiler not associated with the finalproduct streams with a bidirectional vapor-liquid connection. Fully thermally coupled (FTC)configurations are those in which all the vapor requirements of the sequence are supplied by a singlereboiler and the entire reflux by a single condenser. The FTC with an external pre-fractionator is aPetlyuk configuration (Caballero et al., 2013). The thermodynamically equivalent configurationscould be generated from the thermally coupled sequences through moving one column sectionassociated to a condenser and/or a reboiler which provides the common reflux flow rate or the vaporboil up between two consecutive columns. Divided-wall column sequences are other categories,which could be considered to reduce investment costs (Caballero et al., 2013). These configurationsconsist of two columns arranged in a single shell and divided by an internal wall.Earlier approach to synthesis distillation schemes was to use experience-based heuristic rules (Seaderet al., 1977; Tedder et al., 1978; Westerberg, 1985). Heuristic-rule-based methods might lead tofeasible solutions but not necessarily the optimum configuration. A true optimal scheme could befound precisely by a mathematical programming approach. The brief review and work performed byGridhar and Agrawal indicates that in order to achieve the optimum configuration, the first and mostimportant step is to predefine the search space as complete as possible (Gridhar et al., 2010). One ofthe early methods, introducing a superstructure based on “states” and “tasks” was proposed initiallyby Sargent and Gaminibandara (Sargent et al., 1976). This superstructure could be used in mixedinteger linear programming (MILP) (Doherty et al., 2001) or mixed integer nonlinear programming(MINLP) (Caballero et al., 2004 and 2006) to find the optimum sequence. Simple and complexdistillation schemes could be considered with this superstructure.Another systematic approach to synthesize distillation column sequences based on the columnproducts position, which could be distillate, bottoms, or side streams, was proposed by Agrawal(2010). Recently Errico et al. presented a simple 4-step method for the systematic synthesis of thesearch space considering the generation information saving from one configuration to another (Erricoet al., 2009 and 2014). Ivakpour and Kasiri introduced a method which generates simple and/orcomplex distillation columns and bypass streams by introducing a separation matrix (Ivakpour et al.,2008) to synthesize complete as well as reduced sequences. Later Khalili-Garakani et al. extended theseparation matrix method to cover thermally coupled, thermodynamically equivalent, and dividedwallcolumn sequences (Khalili-Garakani et al., 2015).68 Iranian Journal of Oil & Gas Science and Technology, Vol. 5 (2016), No.2Figure 1Three-component distillation sequences considered in this study.1.1. Exergy analysis of distillation sequencesExergy analysis as a tool has been used to study the performance of distillation columns by manyresearchers. Rivero et al. proved that exergy analysis could be used as a tool to provide a good insightinto the process inefficiencies and proving the viability of distillation process modification (Rivero etal., 2004). Besides, this method has proved viable to be used in the synthesis of distillation sequencesA. H. Khalili-Garakani et al./ Three-component Distillation Columns Sequencing … 69to avoid complexity, in laborious systems such as those formed by a large number of components,trays, feeds, and side streams (Kencse et al., 2010).Kencse and Mizsey compared simple and heat integrated forms of direct and indirect sequences andfully thermally coupled schemes for three-component separation mixtures according to cost, exergyloss, and greenhouse gas emissions (Kencse et al., 2010). They reported that an exergy analysis couldpredict the best sequence as predicted by economic and gas emissions studies. There are otherresearchers who used exergy analysis in distillation processes such as Suphanit et al. (2007), whostudied the performance of divided-wall column configurations using exergy analysis) or Pinto et al.(2011), who presented a method for targeting side condensers and reboilers in distillation columnsbased on exergy loss diagrams. Also, Cortez-Gonzalez et al. (2012) analyzed the reduced structuresthat could be generated from simple basic four-component configurations by both economic andexergy analysis. Sun et al. (2012a) used exergy analysis to compare the performance of two differentschemes for organo-silicon monomer distillation process. In another study, they present a five-columnheat integrated methanol distillation scheme using pinch and exergy analysis simultaneously (Sun etal., 2012b).In this work, the whole family of three-component distillation sequences, including simple, complex,thermally coupled, thermodynamic equivalent, divided-wall column, and intensified sequences areconsidered. All sequences (Figure 1) were simulated (based on rigorous simulation), optimized, andcompared according to both economic and exergy analysis indicators. As stated, most of the studieswere mostly reported for the exergy analysis of single distillation column and there are a few reportsof applying the exergy analysis to a large number of columns or distillation sequences (Kencse et al.,2010). According to the authors’ best knowledge, these configurations have never been analyzed andcompared based on an economic study and exergy analysis all together before.2. Methods2.2. Separation matrixThe separation matrix used herein is extensively defied in our previous work (Ivakpour et al., 2008;Khalili-Garakani et al., 2015). In Figure 2, the proposed separation matrix is demonstrated for threeandfour-component feed mixtures. φ is the sign used for the final products which could accept thevalues {I, II, and S}; Ф is the symbol used for sub-mixtures, which could have the values {I, II, andS}. In the separation matrix:1- φ or Φ= {I} is used to demonstrate the column top product (from a condenser);2- φ or Φ = {II} is applied to the column bottom product (from a reboiler);3- And φ or Φ = {S} relates to the mixtures produced as a column side stream.The mixture located in the first column is the original feed and is composed of all final products.Furthermore, the arrays positioned on the same diagonal of the separation matrix have an analogousheavy part. The structure of the distillation configuration could be obtained by the selection of themixture (φ or Φ) options in the separation matrix. For more clarification, the components in eachmatrix array are indicated as subscript at the lower right of each array. Moreover, for the easierprogramming of the algorithm, three more indices are added for each Φ in the matrix { Ф,, ; thefirst index, ψ, indicates the thermal coupling of the product in the relevant distillation columns. Henceeach of the sub-mixture streams that could be a candidate for thermal coupling has an additional ψ70 Iranian Journal of Oil & Gas Science and Technology, Vol. 5 (2016), No.2sign in the lower left of the sub-mixture array associated with it (Ф). ψ could be “0” or “I”,indicating the absence or presence of thermal coupling for its related reboiler or condenserrespectively. The second index, λ, added to the upper left part of the Φ array presents moving,omitting sections, and divided wall between the columns in sequences. This superscript could alsoaccept values “I” or “0”. It must be noted that, in order to make a section movable in a distillationcolumn, the condenser or the reboiler associated with the sub-mixture must initially be omitted.Therefore, in the separation matrix, the related array of the sub-mixture of moving sections shouldhave ψ equated to I. Hence in a systematic programming practice, in order to generate all possiblethermodynamically equivalent configurations, ψ should be checked to be “I” before changing λ foreach sub-mixture. As a result, the arrays which represent moving sections will have two “I” values forboth indices ψ and λ.φ and Ф:{I, II, S}I: Distillate ProductII: Bottom ProductS: Side StreamFigure 2Proposed separation matrix to present different sequences.For intensified sequences, the deleted sections are illustrated by “X” in the separation matrix. λaccepts “X” in the upper left of the array in these cases. In these sequences, the separation could nottake place completely and, for example in sequence Direct-I in Figure 3, a part of component Cappears in product B. The same is true for Indirect-I in Figure 3, in which a part of A is appearing inproduct B. These components are called suspended components and are illustrated by the third indexin the upper right-hand side of the arrays.A. H. Khalili-Garakani et al./ Three-component Distillation Columns Sequencing … 71Figure 3Separation matrices for each distillation sequences presented in Figure 1.At last, for presenting the divided-wall columns, the value of ψ is changed to W. For more tedioussequences with more divided-wall columns, the value of ψ accepts W1, W2… for more clarification.Therefore, separation matrices in which both ψ and λ have value I ({ψ Фλ }), which is the mark of aside column in the sequence, the value of ψ is changed and the separation matrix for the divided-wallcolumn is generated. An example of these kinds of sequences could be seen in Figure 3.72 Iranian Journal of Oil & Gas Science and Technology, Vol. 5 (2016), No.22.2. Exergy analysis of distillation columnsExergy is based on the first and second laws of thermodynamics and is defined as the maximum workwhich could be obtained from a stream or a source of energy until it reaches equilibrium with theenvironment or any reference state. Each stream has an exergy value that is the result of the differencebetween pressure, temperature, and chemical composition of the stream and those of the referencestate. The reference state as defined by Szargut et al. is T0=298.15 K and P0=101.325 kPa (Szargut, etal. 1988). The exergy value of streams degenerates through the process. Thus, due to irreversibilityphenomena in distillation columns, exergy loss is unavoidable. The main irreversibility in distillationcolumns is due to the mixing of the streams with different temperatures, pressures, and compositionson the trays and loss of heat in the condensers and to the environment from the body of the columns.The total exergy of a stream is classified into physical, chemical, and mixing parts, which arecalculated through the following equation (Hinderink et al., 1996):Total exergy:

$ @(8)However, here the exergy loss of the columns is calculated by adding up the exergy loss at each stageof the column. The distribution of the exergy losses along the column (stage by stage) is more usefulin understanding the irreversibility in each part of the column and the improvement of the entiresystem (Suphanit et al., 2007). The exergy losses of a stage in the distillation column could becalculated by carrying out a simple exergy balance around each tray. By calculating the exergy lossesat each stage, the exergy loss diagram of the column could be achieved. Simulation methods areemployed for obtaining the required data for drawing an exergy loss diagram.2.3. Proposed algorithmThe steps of the procedure are described below:· The procedure starts by defining the problem information (n, To, Po, xf, Tf, Pf, and Utilities) andparameter boundaries (xp, optimization parameters).· In the next step, the possible configurations according to the number of components (n) aregenerated and considered. The separation matrix method was utilized for this purpose asdescribed elsewhere (Khalili-Garakani et al., 2015).· The first configuration is then selected and sent to the next step, in which the columns aresimulated by the short-cut method in order to find the initial data comprising of Nt, NF, Rmin, andPCol. The pressure of the columns are optimized here to reach atmospheric pressure as close aspossible, but the boiling point of the liquid in the condenser could remain higher than 35 °C(assume 25 °C for inlet cooling water temperature). Simulated annealing was applied as theoptimization method (Kirkpatrick et al., 1983; Mahmoodpour et al., 2015). For physicalproperty and equilibrium calculations, the Soave-Redlich-Kwang (SRK) equation-of-state wasselected.· In the next step, the rigorous simulations and the outcome of the short-cut method were used asthe initial guess. The inside-out method, according to Seader et al., was used as the rigoroussimulation method (Seader et al., 2011). The reflux ratios of the columns are then optimizedwith the objective of reaching the specified product purity with minimum usage of hot and coldduty in the reboilers and condensers respectively. The simulated annealing was used again atthis stage as the optimization method.· The results of the rigorous calculations (h, s, h0, s0, QH, and QC) were used for the exergyanalysis of distillation columns. The exergy loss for each tray was estimated and the totalexergy loss of the columns (Exdestruction) was evaluated by adding them up in this step. Theformulas and qualities of exergy analysis are presented in the former part.· The results of the rigorous calculations (DCol., QH, and QC) were used for the economic study(Total Annual Cost = annual capital cost + annual operation cost) of the distillation columns.Guthrie’s cost calculation method is employed as modified in Douglas for the economic study(capital cost) (Douglas, 1988). Utility prices for calculating operating costs are as demonstratedin Table 1 (Seider et al., 2010).74 Iranian Journal of Oil & Gas Science and Technology, Vol. 5 (2016), No.2· This procedure was carried out for all the configurations and the results sorted according toeconomic and exergy analysis separately.Table1Utility specification [28].Utility Type Pressure (atm) Temperature (°C) Price ($/GJ)Electricity - - 16.667Cooling Water 1 25 0.254Low Pressure Steam 4.4 144 3.102Medium Pressure Steam 11.2 184 5.257High Pressure Steam 31.6 254 8.174The configurations studied were for mixtures containing three-components with three differentcompositions (F1: [0.4, 0.2, 0.4], F2: [0.33, 0.34, 0.33], and F3: [0.15, 0.7, 0.15]) which are presentedin Table 2.Table 2Different samples considered in this study.αAB=KA/KB αBC=KB/KC αAC=KA/KCVaporFractionPressure(atm)Mixture Components ESI*1.86 4.5 0 2.38 1.28 3.05n-Butane,i-Pentane,n-PentaneM11.04 1.44 0 2.57 2.47 6.35n-Pentane,n-Hexane,n-HeptaneM20.47 1.44 0 1.25 2.65 3.31i-Pentane,n-Pentane,n-HexaneM3* ESI=αAB/αBC [4].3. Results and discussionTable 3 presents the ranking of the sequences presented in Figure 1 for different feed conditions.Also, in Table 4, the economic study and exergy analysis of the first three sequences under eachcondition are presented.Table 3The ranking of configurations for M1, M2, and M3 at different feed compositions.M1F1 F2 F31 Indirect-DWC Direct-TC Indirect-DWC2 Indirect-TE Direct Indirect-TE3 Symmetrical-DWC Indirect-TC Indirect-TC4 Symmetrical-TC2 Indirect-DWC Direct5 Symmetrical-TC3 Direct-DWC Direct-TC6 Direct Indirect-TE Symmetrical-TE57 Symmetrical-TE4 Direct-TE IndirectA. H. Khalili-Garakani et al./ Three-component Distillation Columns Sequencing … 758 Symmetrical-TE3 Indirect Direct-DWC9 Symmetrical-TE2 Symmetrical-DWC Direct-TE10 Symmetrical-TC1 Symmetrical-TC3 Symmetrical-TC111 Indirect Symmetrical-TC2 Symmetrical-TE212 Symmetrical-TE1 Symmetrical Symmetrical-TC213 Indirect-TC Symmetrical-TE4 Symmetrical-TE114 Symmetrical Symmetrical-TE3 Symmetrical-DWC15 Direct-DWC Symmetrical-TC1 Symmetrical16 Direct-TE Symmetrical-TE2 Symmetrical-TC317 Direct-TC Symmetrical-TE1 Symmetrical-TE418 Indirect-IC Symmetrical-TE5 Symmetrical-TE319 Symmetrical-TE5 Indirect-IC Indirect-IC20 Direct-IC Direct-IC Direct-ICM2F1 F2 F31 Direct-TC Symmetrical-DWC Symmetrical-TE22 Direct-DWC Symmetrical-TC3 Symmetrical-TC13 Symmetrical-TC2 Direct-TC Symmetrical-TE14 Symmetrical-TE4 Symmetrical Indirect-DWC5 Direct-TE Direct-DWC Symmetrical6 Symmetrical-TE3 Direct-TE Indirect-TE7 Symmetrical-DWC Indirect-DWC Indirect-TC8 Indirect-DWC Indirect-TE Symmetrical-DWC9 Indirect-TE Direct Symmetrical-TC310 Symmetrical-TC3 Symmetrical-TC2 Direct-DWC11 Symmetrical Symmetrical-TE4 Direct-TE12 Direct Symmetrical-TE3 Direct13 Indirect-TC Indirect-TC Indirect14 Indirect Indirect Direct-TC15 Symmetrical-TE2 Symmetrical-TE2 Symmetrical-TC216 Symmetrical-TC1 Symmetrical-TC1 Symmetrical-TE417 Symmetrical-TE1 Symmetrical-TE1 Symmetrical-TE318 Indirect-IC Symmetrical-TE5 Symmetrical-TE519 Symmetrical-TE5 Indirect-IC Indirect-IC20 Direct-IC Direct-IC Direct-ICM3F1 F2 F31 Direct-DWC Symmetrical-TE2 Indirect-DWC2 Direct-TE Direct-DWC Symmetrical-TE23 Indirect-DWC Direct-TE Indirect-TE4 Symmetrical-TE2 Indirect-DWC Indirect-TC5 Indirect-TE Indirect-TE Direct-TC6 Direct Symmetrical-TE1 Direct-TE7 Symmetrical-TC1 Symmetrical-TC1 Direct-DWC8 Symmetrical-TE1 Direct Symmetrical-TC19 Indirect-TC Direct-TC Direct10 Direct-TC Indirect Symmetrical-TE176 Iranian Journal of Oil & Gas Science and Technology, Vol. 5 (2016), No.211 Indirect Indirect-TC Indirect12 Symmetrical Symmetrical Symmetrical-TE413 Symmetrical-TC2 Symmetrical-DWC Symmetrical14 Symmetrical-DWC Symmetrical-TC3 Symmetrical-TE315 Symmetrical-TE4 Symmetrical-TC2 Symmetrical-DWC16 Symmetrical-TC3 Symmetrical-TE4 Symmetrical-TC317 Symmetrical-TE3 Symmetrical-TE3 Symmetrical-TC218 Direct-IC Direct-IC Symmetrical-TE519 Symmetrical-TE5 Indirect-IC Direct-IC20 Indirect-IC Symmetrical-TE5 Indirect-ICTable 4The result of total annual cost ($/y) and exergy loss rate (GJ/hr) for the best three sequences under different feedconditions.Exergy loss rate(GJ/hr)Mixture Composition Sequences TAC ($/year)1st Indirect-DWC 293,472.592 0.675F1M12nd Indirect-TE 296,297.113 0.6763rd Symmetrical-DWC 303,743.586 0.6791st Direct-TC 340,502.266 0.229F2 2nd Direct 367,942.217 0.2553rd Indirect-TC 3778,841.474 0.6291st Indirect-DWC 508,593.831 1.531F3 2nd Indirect-TE 512,115.351 1.5353rd Indirect-TC 526,700.303 0.6871st Direct-TC 138,095.912 0.696F1M22nd Direct-DWC 142,216.070 0.7203rd Symmetrical-TC2 144,355.762 2.6541st Symmetrical-DWC 170,791.224 0.599F2 2nd Symmetrical-TC3 172,106.681 0.6003rd Direct-TC 175,504.430 0.3511st Symmetrical-TE2 196,042.597 1.177F3 2nd Symmetrical-TC1 212,178.195 1.1873rd Symmetrical-TE1 212,217.274 1.1881st Direct-DWC 278,968.356 0.628F1M32nd Direct-TE 279,719.402 0.6293rd Indirect-DWC 281,628.454 0.3771st Symmetrical-TE2 326,486.558 0.956F2 2nd Direct-DWC 329,243.256 0.7853rd Direct-TE 329,686.667 0.7861st Indirect-DWC 463,035.983 0.342F32nd Symmetrical-TE2 469,954.929 0.718A. H. Khalili-Garakani et al./ Three-component Distillation Columns Sequencing … 77Exergy loss rate(GJ/hr)Mixture Composition Sequences TAC ($/year)3rd Indirect-TE 472,286.012 0.344When the feed content of component B is low, the composition of B in the liquid feed of the sidestripper is much lower than that of the vapor feed of the side rectifier. This is due to liquid feed of theside stripper being diluted by a significant amount of component A, while in the vapor feed of the siderectifier, this is done with the same amount of component C. As a result, for producing component Bwith the same specification, vapor traffic in the side stripper is significantly more than side rectifier.Therefore, more heat could be supplied at a mid-temperature of TB in side stripper configuration (incomparison to the lower amount of rejected heat in the condenser at temperature TB in side rectifier).This is the reason why Indirect-TE and Indirect-DWC perform better for M1 and composition F1.Also, when the content of the middle component B is high in the feed, these two configurations havesuperior performance compared to other sequences, with the only exception of M2 in which ESI≈1.According to Malone et al. (1985), when component relative volatilities are close (αAB, αBC), as in M2(F1 and F2), direct sequence is one of the best, as also demonstrated by the present results. As αBapproaches αA, the chance for direct family to be one of the preferred sequences increases. However,this is not the case when component B content increases. When αAB is low, for the separation of Afrom B, a large amount of vapor is needed; however, the condenser temperature for pure A (TA) isnearer to the B bubble point (TB) than to pure component C reboiler temperature (TC). As a result, it isbetter to supply the required heat for the separation of A from B at mid temperature level (TB). Inconfigurations like symmetrical-TC3 (Petlyuk sequence), supply of heat at TB is not possible and thisleads to the better performance of sequences such as indirect-TE in comparison to symmetrical-TC3.This is true for divided-wall column sequences which are generated from these configurations.Symmetrical (Brugma or pre-fractionator) sequence and the other sequences generated from it(thermally coupled and equivalent thermodynamics) have their best performance in M2, in whichESI≈1. The comparison of thermally coupled configurations (symmetrical-TC1, TC2, and TC3) withside stripper, side rectifier, and other symmetrical configurations illustrate that side stripper and siderectifier configurations have better performance for M1 (ESI>1) and M3 (ESI<1), and only in M2(ESI≈1), the thermally coupled sequences present the reduction of energy consumptions. Similarresults are presented in the work by Agrawal and Fidkowski (1999), in which they calculate theminimum total amount of vapor in sequences in minimum reflux condition. Thermally coupledsequences for feed M2 and F3 composition illustrate 34% reduction of energy consumption incomparison to simple sequences (direct and indirect).The results of thermodynamically equivalent configurations presented by Agrawal and Fidkowski(1998) (symmetrical-TE1-TE4) is nearly the same as thermally coupled configurations under all feedconditions considered in this study. In these configurations, reboilers and condensers are located ondifferent columns; the column at a high pressure has a reboiler, and the column at a low pressure has acondenser; in this way, the vapor stream could be flown from the column at a higher pressure to theone at a lower pressure. The change to the structure of the sequence made it more operable and easyto control. Comparing them to the symmetrical-TC3 illustrates that symmetrical-TC3 sequenceperforms better for M1 with F1-F2 feed composition, and symmetrical-TE1 and symmetrical-TE2 arebetter for F3 feed composition. For M2 and feed F1, symmetrical-TE3 and symmetrical-TE4 aresuperior, while symmetrical-TC3 outperforms for feed F2, and symmetrical-TE1 and symmetrical78Iranian Journal of Oil & Gas Science and Technology, Vol. 5 (2016), No.2TE2 perform better for F3. In M3, symmetrical-TE1 and symmetrical-TE2 perform better at all threedifferent feed compositions.Agrawal and Fidkowski (1998 and 1999) presented symmetrical-TE1-TE4 configurations andanalyzed them by the minimum total amount of vapor in sequences in a minimum reflux condition.Then Jiménez et al. (2003) analyzed them by rigorous methods and compared their heat duty. Incomparison to their work, the research presented here uses more accurate total cost and exergy lossanalysis, which justifies some of the differences in ranking of the sequences. The column diametercalculation procedure considered herein in TAC analysis is one of the main reasons behind thedifferences between the two findings.Furthermore, it should be noted that some of the configurations considered herein are not present inthe works of Caballero and Grossman (2001 and 2004), which employs a suggested superstructureand optimizes the tray sections and energy performance of configurations.Figure 4a presents the number of occurrences of the best three sequences for all the cases studiedhere. Indirect-DWC sequence has the largest number of occurrences followed by Direct-DWC,Direct-TC, Indirect-TE, and Direct-TE sequences respectively.Also in Figure 4b, the distribution of the best sequence among different categories of configurations isillustrated. As presented, DWC sequences have the biggest part and the basic sequences have thelowest part among the best configurations.Figure 5 illustrates the exergy loss diagram of symmetrical configurations (Brugma configurations)for different feeds (M1-M3) and compositions (F1-F3). Brugma sequence was considered herebecause from this sequence all the other configurations could be derived. As demonstrated, increasingB content in the feed raises the peak in the exergy loss diagram. For M1 (ESI>1), the maximum lossis in the upper feed of the second column. At the time (ESI≈1 (M2)), there were two peaks: one in theupper feed of the second column and the other in the reboiler. At last for M3, the peaks are located onthe lower feed and the condenser of the second column.a)A. H. Khalili-Garakani et al./ Three-component Distillation Columns Sequencing … 79b)Figure 4a) Number of occurrences of the best three configurations in different samples and b) distribution of the bestsequences among different configuration categories.The location of peaks in the diagrams could be found by the relative volatility of the components. Asillustrated in Table 2 and Figure 5, the peaks are located in the place (section) where the feed withhigher relative volatility enters the second column. It is due to the superior separation ability of themixture with greater relative volatility in the pre-fractionator (first column). Thus in the next column,the streams with much different compositions encounter each other, and as a result the exergy lossesdue to mixing is increased. Since, αAB is higher in M1 (ESI>1), there is a peak in the upper feed of thesecond column. However, the relative volatility becomes similar in M2 (ESI≈1) in the prefractionator,where the separations (A/B and B/C) take place in the same order. Hence separation inthe next column would be easier, and, as a result, the exergy loss is decreased. This effect is moresignificant when the content of the middle component (B) is lower in the feed. In these configurations,the amount of loss in the upper (rectifier) and lower (stripper) sections of the second column arenearly the same and the distribution of losses is more monotonous.As stated before, when the amount of αAB is low (M3: ESI<1), a large amount of vapor is required forthe separation of A from B. As a result, the exergy loss in the condenser is increased and a peak couldbe seen in the condenser.Therefore, by these figures the designers could easily find the weak points in each column of thesequence and employ the exergy loss diagram for improving the performance of the sequence.Furthermore, the changes to the structure of the columns in these places similar to thermal coupling ofthe streams between columns, generating thermodynamically equivalent structures by movingsections in these areas, or using internal wall (DWC) could reduce the exergy loss of the system (aspresented in the results in the former section).Basic11%Thermally Coupled25%ThermodynamicallyEquivalent28%DWC36%Chart Title80 Iranian Journal of Oil & Gas Science and Technology, Vol. 5 (2016), No.2Figure 5Exergy loss diagram of the symmetrical sequence (Brugma) for different feeds (M1-M3) and compositions (F1-F3).In addition, the knowledge of the weak points of the sequences and structural changes could lead to asearch space reduction algorithm. This algorithm helps designers to analyze a much smaller searchspace containing only near optimal sequences, which could be sufficient to find an overall optimal ncomponentconfiguration. The search space reduction algorithm is out of the scope of this paper andwould be presented in future works.4. ConclusionsThe analysis of the samples illustrates that the TAC of the sequences is totally dependent on theamount of the intermediate component present in the feed. By increasing the amount of theintermediate component, TAC is increased for each sequence. Also, despite expectations, the Petlyuksequence (symmetrical-TC3) only performs well in M2 (ESI≈1) and for F2 composition; itdemonstrates poor performance for other conditions (like different compositions of M3). Incomparison to economic study, exergy analysis is simpler in calculation and only requires someA. H. Khalili-Garakani et al./ Three-component Distillation Columns Sequencing … 81physical properties, which could easily be acquired; also, the exergy loss diagrams could givedesigners an insight into the weak parts of the systems and help with improving the performance ofthe processes. Knowing the weak points in each column of the sequence could be used for thestructural changes of the sequence, and could lead to the generation of new configurations. The resultspresented that changes such as thermal coupling of the streams between columns, generatingthermodynamically equivalent structures by moving sections in these areas, or applying divided-wallcolumns could reduce the exergy losses of the system (Khalili-Grakani, 2016).At last, according to the ability and flexibility of the separation matrix in changing the structure of thesequence, the method could be easily expanded to a larger number of components and other kinds ofsequences like multi-effects, pump around, compressor-aided separations, and internal heat integrateddistillation systems (HIDIC), which would be considered in future works. The detailed optimizationprocedure is beyond the scope of this work and will be presented in future works.NomenclatureSymbolsΔ*+, : Standard Gibbs energy of formation [kJ/mol]Extotal : Total exergy content [kJ/kg]Exphys. : Specific physical exergy [kJ/kg]Exchem. : Specific chemical exergy [kJ/kg]Ĕxchem : Standard chemical exergy [kJ/mol]ExMix. : Specific exergy of mixing [kJ/kg]h : Specific enthalpy [kJ/kg]ho : Specific enthalpy at T0, p0 [kJ/kg]I : Top productII : Bottom productIII : Eliminated mixture in crossover complete sequencesL : Liquid fractionn : Number of chemical speciesΦ : All possible states for sub-mixturesφ : All possible states for product typepo : Pressure of the reference state [101.325 kPa]R : Gas constant [kJ/mol.K]S : Side streams : Specific entropy [kJ/kg.K]so : Specific entropy at T0, p0 [kJ/kg.K]To : Temperature of the reference state [298.15 K]V : Vapor fractionx : Mole fraction of speciesSuperscriptsa, b : Presenting suspected components in each stream82 Iranian Journal of Oil & Gas Science and Technology, Vol. 5 (2016), No.2λ : Sign of moving section or omitting section in related distillation columnsSubscriptψ : Sign of thermal coupling of the product in related distillation columnsr, k : Presenting components in each streamReferencesAgrawal, R., Fidkowski Z. 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